DE19519753C2 - Optical scanner - Google Patents

Description

The present invention relates to an optical Scanner for use in a laser beam printer or other facilities.

An optical scanner like the one in a laser beam printer or other equipment is used conventionally, includes a light source such as B. a semiconductor laser, a Collimator lens, the one from the light source Beam of light aligns a rotating polygonal Mirror that scans the aligned light beam deflects, and an imaging lens that the deflected light focused around a beam spot on a scanning surface to build.

Optical scanner with a light source for emitting a Light beam and a deflecting device that blocks the light beam distracts while doing it at uniform angular velocity rotates with those with an imaging lens aspherical surfaces in a main scan cross-section Beam spot on a scan surface by focusing the Light beam that has been deflected by the deflecting means have become known in a variety of ways (see e.g .: Akira Arimoto: Laser scanning system using a rotationally asymmetric aspheric surface, Applied optics, February 20, 1991, Vol. 30, No. 6, pp. 699-703; U.S. 5,329,399; U.S. 5,128,795; US 4 971 411).  

An imaging lens must have the following two aberrational characteristics:

• A) a specified negative distortion value, which it is necessary to scan at a uniform speed reach, and
• B) a smaller field curvature, which is the beam spot size reduced to close to the diffraction limit, thereby creating a flat Provide image plane.

The imaging lens can be one or more Lens elements can be composed. If good Aberration characteristics are needed, many Lens elements used; if the cost is important used a single lens. To further improve Achieving aberration characteristics are often today used imaging lenses with an aspherical surface, as typically taught in JP-A-92/50908.

It is well known that everyone has a spherical lens surface Make the same curvature. In contrast, one aspherical  Lens surface different local curvatures different places. Therefore, that in JP-A-92/50908 described aspherical imaging lens a problem in that if the beam of light passing through it has a diameter larger than a certain value, the local curvature itself within a Cross section of the beam depending on the location on the aspherical surface changed. As a result, the Wavefront of the beam through the aspherical Surface was subjected to a transformation, so disturbed that the Image characteristics are affected, which in turn the shape of the beam spot is deformed. The amount Asphericity can be from one extreme to one negligible deviation from a spherical surface has, on the other hand, one from concave to convex or reversely changing diffraction point, in the center of the optical axis and on both edges, range. The Deformation of the beam point is particularly the latter Case noticeable.

With the recent ones aimed at higher resolution Advances in laser beam printer technology exist a growing need for optical scanners that still can form smaller beam spots. A gaussian ray means that to get a smaller beam spot with a lens to generate a beam with a certain focal length a wider divergence angle must be dimmed. The means a beam of large diameter rather than one small diameter must be inserted into the lens. Therefore, a further improvement in the resolving power can only be achieved with difficulty by laser beam printers, before not solving the problem outlined in the previous paragraph is.

The one used in a conventional optical scanner Imaging lens has the following problems.  

• 1. The optical magnification of the imaging lens in the Subscan direction is in the center and the two Edge areas of the lens differ, resulting in a inconsistent beam spot size in the subscan direction leads. In addition, a larger number of lens elements used for uniform optical magnification to reach in the subscan direction.
• 2. The thickness of the imaging lens in the axial direction is comparatively larger than the lens height in subscans Direction so that internal dispersion tends to occur during the Forming the plastic lens to occur what a Relocation of the focus or impairment of the imaging characteristics.
• 3. The main scan cross section of the imaging lens is in Center of lens thick, but narrow on both edges, and the difference is so big that when molding the lens out Plastic the molten polymer runs unevenly, so that internal dispersion develops.
• 4. There is a collimated beam in the imaging lens is introduced, this must have a large positive refractive power have, but then the thickness of the Main scan cross section of the lens in the center so much larger than on both edges that the thickness profile of the lens is extreme is unequal.
• 5. Merely composed of axially symmetrical Components, the imaging lens has only a small one Degree of freedom in correcting aberrations and no satisfactory correction for field curvature and Scan at uniform speed in both the Main as well as the subscan direction. In addition, the imaging lens from a larger number of lens elements  be composed to a satisfactory correction of To obtain aberrations.
• 6. If the reflective surface of the distracting If the elements are tilted, the scan line is moved.
• 7. Because the imaging lens has a constant curvature in the Has subscan direction, the field curvature can be in this Direction cannot be reduced adequately. The must also imaging lens from a larger number of lens elements be constructed to ensure that the field curvature developing in the subscan direction, sufficient is reduced.
• 8. One formed on both sides from curved surfaces imaging lens requires high production costs and needs in addition a high degree of precision in the alignment the optical axes of the two surfaces.
• 9. If the subscan section of a surface of a imaging lens is linear, the degree of freedom must optical design in the subscan direction for correction the field curvature will be spent and it is no longer possible to produce a uniform beam spot size.

It is therefore the object of the present invention to provide a to provide optical scanners that provide an imaging Lens with aspherical surfaces used, its parameters fulfill a specific relationship in order to be satisfactory imaging characteristics without deformation in shape to ensure the beam spot while the scanner is moving Use at higher resolution is suitable.

This object is achieved by the provision according to an optical scanner with improved properties the independent claim 1 solved. More details,  Aspects and advantages of the present invention result from the dependent claims, the description and the Drawings.

The present invention relates generally to an optical scanner which has a light source for emitting a light beam, deflection elements which, when they rotate at a uniform angular velocity, deflect the light beam, and an imaging lens for forming a beam spot on a scanning surface by focusing the light beam, deflected by the deflecting elements, wherein the imaging lens has an aspherical surface in the main scanning direction, and the improvement in which the parameters e, n, w, and ρ relating to the aspherical surfaces satisfy the following condition , having:

being the relationship

applies, and
c _i (V _i ): curvature of the lens surface S _i at height v _i above the optical axis;
e _i : distance between lens surfaces S _i and the scanning surface;
g: main scanning radius of the beam spot at zero image height;
n _i : refractive index of the imaging lens forming the lens surface S _i ;
S _i : i th lens surface;
u _i : coefficient that indicates whether the lens surface S _{i is} an entrance surface or an exit surface with
u _i = 1 (entrance surface)
u _i = -1 (exit surface)
v _i (ys): height above the optical axis of the point at which the main beam at image height y _s crosses the lens surface S _i ;
w _i : main scan cross-sectional radius of a light beam on the lens surface S _i , which passes along the optical axis of the lens surface S _i ;
y: coordinate indicating the height above the optical axis in the main scanning direction;
y _s : image height on the scanning surface; and
ρ _i (Y _s ): measure of the change in curvature at the point where the main beam at image height y _s crosses the lens surface S _i , calculated by deriving the curvature c _i with respect to y.

In certain embodiments of the invention, the optical scanners any of the following additional Have structural features.

• 1. The scanner further fulfills the following condition in the effective area of the main scan cross section of the lens surface S _{i of} the imaging lens:
  in which
  Δz _i (y): axial displacement of the lens surface S _i at the height y above the optical axis;
  b _i : distance of a deflection point of the deflection elements from the lens surface S _i ; and
  a: Distance of a deflection point from the scanning surface
  is.
• 2. The scanner further fulfills the following condition in the subscan section of the imaging lens:
  h / t <2
  in which
  t: thickness of the imaging lens in the direction of the optical axis; and
  h: height of the imaging lens in the subscanning direction
  is.
• 3. The scanner further fulfills the following condition in the effective area of the main scan cross section of the imaging lens:
  t _max / t _min <2
  in which
  t _max : maximum thickness of the imaging lens in the direction of the optical axis; and
  t _min : minimum thickness of the imaging lens in the direction of the optical axis
  is.
• 4. The light beam penetrating the imaging lens is convergent in the main scan cross section.
• 5. The imaging lens has the main scan direction and Subscanning device different refractive powers.

In the embodiment according to 5) the deflection point and the The scanning surface in the subscan section should be optically conjugated. In another embodiment according to 5), the curvature of a Cross section parallel to the subscan section along the Main scanning direction in the effective area of the imaging Lens in at least one of its surfaces continuously change.

In the latter case, the subscan cut in linearly at least one surface of the imaging lens his. Alternatively, the curvature of one to Subscan section parallel section along the Main scanning direction in the effective area of the imaging Change the lens in its two surfaces continuously.

With these structural features, the present one Invention the following outstanding functional advantages.

The imaging lens with aspherical surfaces is like this designed to focus on the aspherical surface  related parameters meet the specified relation, whereby the shape of a main scan cross section of a Beam point is designed so that its deformation is none practical problems.

The imaging lens can be adapted to a specific shape be, creating a uniform optical magnification in the Subscanning direction between the imaging point in the Environment of the deflecting surface of the deflecting elements and the imaging point is achieved on the scanning surface, so that both the beam spot size and the resolution are uniform.

The cross section of the imaging lens can also be at a certain form, which the Refractive index distribution in one to the direction of the Beam migration perpendicular direction reduced. This protects effective before a focus or a shift Impairment of the imaging characteristics.

The shape of the effective area of the main scan cross section imaging lens can have such a thickness t that the Molten synthetic polymer tendency while the formation to flow unevenly is inhibited to the Prevent internal scatter from occurring.

Also, the light beam is inserted into the imaging lens converged in the main scan cross section and therefore requires the imaging lens only a small refractive power. As a result the thickness of the lens can be brought almost to uniformity become.

The imaging lens can be further different Have power in the main and subscan directions in which case the correction of aberrations in the Main scan direction regardless of the correction in  Subscanning can be made. This contributes to one greater degree of freedom in the optical construction.

The deflection point and the scanning surface can be in the Subscan sections are optically conjugated. Therefore, even if the rotating polygonal mirror or Lens mirror has a tilting reflective surface that Position of the beam spot on the scan surface in the Do not change subscanning direction and there will be no transfer of the scan line are coming.

The exit surface of the imaging lens is preferably designed so that the curvature of one to Subscan section parallel section along the Main scanning direction in the effective area of the imaging lens continuously changing, and thus the curvature of a to the subscan section parallel section on each Place in the effective area of the imaging lens on one desired value can be set. This allows one complete correction of the curvature of the field in the Subscan direction can be present.

One of the two surfaces of the imaging lens can be in the Subscan section to be linear, which is an easy manufacture the imaging lens allowed and thereby the cost of their Production lowers. If a single lens two optically has curved surfaces, the accuracy of the relative Positions of the optical axes of these two surfaces Problem, and is achieving strict alignment nevertheless required between the two optical axes. If however, the imaging lens as in the subscan section Planoconvex lens is designed to meet such a condition not be met for the subscan cut.

Finally, both surfaces of the imaging lens Have curvatures in the subscan section  change continuously, creating an additional Degree of freedom in optical design in the subscanning direction is conditioned. Thus, it can be completely constant Beam spot size can be generated in the subscanning direction.

Various preferred embodiments and aspects of the present invention result from the following detailed description in conjunction with the attached Drawings in which:

Fig. 1 is a perspective view of an optical scanner according to a first embodiment of the present invention;

Fig. 2 is a diagram showing how a light beam is deflected at the deflecting mirror used in Example 1;

Figures 3a and 3b are diagrams showing the beam paths of the two beams that pass through an aspherical lens;

Fig. 4a, 4b, and 4c are waveform diagrams showing the intensity distribution in a beam spot;

Fig. 5 is a graph showing the intensity profile of a secondary "peak" of a light beam;

Fig. 6 is a cross section of an imaging lens in the sub-scanning direction;

Fig. 7 is a graph showing the cooling rate profile of an imaging lens;

Fig. 8 is a diagram showing two distributions of the refractive index of a plastic lens;

Fig. 9 is a cross section of a ribbed imaging lens in the subscanning direction;

Fig. 10 is a diagram showing the concept of optics used in Example 1;

Fig. 11 is a cross sectional view showing the structure of the optics used in Example 1;

Fig. 12 is a plotter plot of the aberration curves obtained with an optical scanner according to Example 1;

Fig. 13 is a diagram which records the values of a relationship of change in curvature, and other parameters associated with the imaging lens of Example 1;

Fig. 14 is a graph plotting the amounts of axial displacement of the surfaces of the imaging lens used in Example 1;

Fig. 15 is a graph plotting the change in beam spot size that occurred in Example 1;

FIG. 16a to 16e are diagrams showing different shapes of the imaging lens when fabricated with "bending", illustrate;

Fig. 17 is a perspective view showing the optical scanner according to a second example of the present invention;

Fig. 18 is a cross sectional view showing the structure of the optics used in Example 2;

Fig. 19 is a graph showing the aberration curves obtained with the optics of Example 2;

Fig. 20 is a plotter of the values of a relationship between change in curvature and other associated parameters to the imaging lens used in Example 2;

Fig. 21 is a graph plotting the amounts of axial displacement of the surfaces of the imaging lens used in Example 2; and

Fig. 22 is a Plotterdarstellung the change in the beam spot size, which has occurred in Example 2.

Exemplary embodiments of the present invention will now be described with reference to the accompanying Drawings explained.

Fig. 1 is a perspective view showing Example 1 shows the structure of an optical scanner according to the present invention. An outgoing from a light source (semiconductor laser) light beam 1 is stopped down by a Blendendiaphragma 7, converted into a slightly convergent beam by a collimator lens 2 and subjected to the focusing action of a cylindrical lens 3 in only the sub-scanning direction. The term “subscanning direction” means a direction that is parallel to the axis of rotation of the deflection elements, such as a rotating lens mirror 4 . A direction orthogonal to both the subscanning direction and the optical axis is referred to as the main scanning direction. The beam falls on the entry surface of the rotating lens mirror 4 , which acts as a deflection element. Image formation only occurs in the subscanning direction in the vicinity of the reflecting surface. The beam emerges through the exit surface after being reflected by the reflecting surface. Both entry and exit surfaces have refractive power only in the main scanning direction and are concave or convex-cylindrical surfaces. The reflective surface of the lens mirror 4 is flat. The incident beam is deflected while the lens mirror 4 rotates. The deflected beam is then subjected to the focusing action of an imaging lens 5 and forms a beam spot on a scanning surface 6 .

Fig. 2 shows how the beam is deflected while the lens mirror 4 is rotating. The entrance surface S _a and the exit surface S _{c of} the lens mirror are designed so that a beam that scans the scanning center crosses these surfaces perpendicularly. The reflecting surface S _b is designed such that the beam that scans the scanning center strikes this surface at an angle of 45 °. The rotating axis 0 of the lens mirror 4 lies in the reflection surface S _b and intersects it at a point at which the beam that scans the scanning center is reflected. The optical axes of the entrance surface S _a and the exit surface S _c coincide with the beam path of the beam that scans the scanning center. The lens mirror 4 rotates about the axis 0 and successively passes through phases I, II and III, which are indicated by the dashed line, the solid line and the dash-dotted line. While the lens mirror 4 rotates in this way, the incident beam L falls at different points at different angles on the entrance surface S _a , whereupon it is refracted by the latter in order to be deflected. The beam is reflected by the reflecting surface S _b to be deflected at a larger angle and is then refracted by the exit surface S _c so that it emerges again as a deflected beam, as symbolized by M ₁ , M ₂ , or M ₃ .

The structure of the imaging lens 5 used in Example 1 is shown in cross section in FIG. 9 and will now be described in detail. The entrance surface R ₁ and the exit surface R _{2 of} the imaging lens 5 used in Example 1 are aspherical in the main scan cross section (the "main scan cross section" is a plane which contains the optical axis and which is parallel to the main scan direction). These aspherical surfaces have different curvatures at different points. If the deviation is so large that the curvature varies even within the beam diameter range, the wavefront of the beam which is subjected to conversion through the aspherical surfaces is disturbed so that it is no longer spherical and its imaging characteristics are impaired. To avoid this problem, the asphericity parameters e, n, w, and ρ of the imaging lens 5 used in Example 1 meet the following condition:

being the relationship

applies, and
c _i (v _i ): curvature of the lens surface S _i at height v _i above the optical axis;
e _i : distance between lens surface S _i and the scan surface;
g: main scanning radius of the beam spot at zero image height;
n _i : refractive index of the image-forming lens forming the lens surface S _i ;
S _i : i th lens surface;
u _i : coefficient indicating whether the lens surface S _{i is} an entrance or an exit surface;
u _i = 1 (entrance surface)
u _i = -1 (exit surface)
v _i (y _s ): height of the point at which the main beam crosses the lens surface S _i at image height y _s , above the optical axis;
w _i : main scan cross-sectional radius of a light beam on the lens surface S _i , which runs along the optical axis of the lens surface S _i ;
y: coordinate representing the height above the optical axis in the main scanning direction;
y _s : image height on the scanning surface; and
ρ _i (Y _s ): measure of the change in curvature at the point where the main beam at image height y _s crosses the lens surface S _i , calculated by deriving the curvature c _i to y,
is.

Within this design, the shape of the beam spot is deformed little so that there are no practical problems. A specific procedure of the calculations is given below to prove this point with a typical example. As shown in Fig. 3a, it is assumed for the sake of simplicity that the entrance surface S _{d of} the imaging lens 5 is flat, while the exit surface S _{e is} paraxially flat, except that it is provided with an aspherical displacement. A parallel beam passes through the imaging lens 5 along the optical axis. The main scan cross-sectional radius of the beam at the exit surface S _e is denoted by w. The cross-sectional radius w of the beam means the radius of a geometric shape that is formed by connecting the points in the cross-section of the beam where the beam intensity = 1 / e ^{2 of} the intensity at the center of the beam. The point at which the exit surface S _e crosses the optical axis is taken as the origin, and the z-axis extends along the optical axis, while the y-axis extends in a direction normal to the optical axis. Surfaces with a variable curvature are indicated by a curve 3 . Degrees represents. Therefore, the exit surface S _e can be expressed as:

z = ky ³

where k is a constant

Then the change in curvature ρ is paraxial a cubic derivative from z to y, as expressed by:

ρ = 6k

If one takes into account that the beam has a thickness with the radius w, it can be interpreted as a bundle of individual beams. Based on this assumption, let the individual beam N, which passes through the distance a distance w away from the optical axis, be followed. If the exit surface S _e inclines by 3kw ² at the height w above the optical axis and if the imaging lens 5 has a refractive index of n, the angle α is the single beam emanating from the exit surface S _e with the optical axis , approximately expressed by:

α = 3kw ² (n - 1)

The degree of change in curvature ρ is therefore linked to angle α by:

α = ρw ² (n - 1) / 2

The point U, at which the single beam N intersects a plane 9 , which is a distance q away from the exit surface S _e , deviates from the point T, where the same single beam intersected the plane 9 , if the exit surface had no aspherical displacement, and the deviation m is given by:

m = ρqw ² (n - 1) / 2

The central single beam moves directly on the optical axis without experiencing any dislocations in the Y direction. The above calculations show that if the beam with radius w is interpreted as a bundle of individual beams, a single beam is caused to deviate on plane 9 to a surface whose curvature changes with dimension ρ, the maximum deviation being equal to m is.

The above explanations relate to the case in which a parallel beam reaches plane 9 without forming a beam point. In practice, the beam should ideally focus at a point on the scanning surface 6 , and Fig. 3b shows what happens when a beam focusing at a point on the scanning surface 6 passes through an imaging lens with an aspherical shift. As in FIG. 3a, the exit surface S _{e of} the imaging lens 5 is aspherical. If the distance between the exit surface S _e and the scan surface 6 is designated by e, the point U at which the single beam N intersects the scan surface 6 deviates from the position T at which the same beam intersected the scan plane 6 if the exit surface S _{e would} not have a spherical displacement, and this deviation m results as:

m = ρew ² (n - 1) / 2

If the deviation m is excessively large, the individual individual beams in the beam will not coincide at one point on the scanning surface 6 , even if there is a focal point on this surface, and instead a deformed beam point will occur, the imaging characteristics of which are impaired.

Next, the relationship between the single beam deviation m on the scanning surface 6 and the deformed shape of the beam spot based on the results of a simulation will be discussed. The letter g is used here to express the radius of the beam spot on the scanning surface 6 . The term "radius of the beam" means the radius of a geometric shape obtained by connecting the points at which the beam intensity = 1 / e ^{2 of} the intensity at the center of the beam. The profile of the cross-sectional intensity of the beam point is essentially only determined by the ratio of the individual beam deviation m and the beam point radius g (m / g). As shown in Figures 4a, 4b, and 4c, the increasing value of m / g is accompanied by a corresponding increase in the secondary peak F on the beam side. Figure 5 is a graph plotting the intensity of the secondary peak relative to the central intensity of the beam against m / g. If the intensity of the secondary peak increases, neighboring pixels are also illuminated by the beam, so that the resolving power of the optical scanner is impaired. In addition, a laser printer using this optical scanner will produce blurry prints. In the case of a print pattern composed of fine pixels, the contrast will decrease, so that the print quality is poor. According to the experiment carried out by the inventors, the intensity of the secondary peak should preferably be less than 1 / e ^{2 of} the central intensity in order to ensure satisfactory imaging characteristics for the optical scanner and to guarantee satisfactory image quality with a laser beam printer. Therefore, according to FIG. 5, the following condition should advantageously be fulfilled:

| m | / g <2.5

and thus:

| ρ | ew ² (n - 1) / 2g <2.5

If the optical scanner is in a color printer or other Printers that have even finer tonal gradations need to be used is the value of | m | / g desirably much smaller.

If more than one aspherical surface is used, the deviation of the single beam on the scan surface is the accumulation of the deviations resulting from the changes in the curvatures of the respective aspherical surfaces, provided that the direction in which single beams are reflected is between the Entry and exit surfaces differ. Thus, using the coefficient u that determines whether a particular lens surface is the entrance or exit surface, the imaging lens should meet the following condition:

in which

u _i = 1 (entrance surface)

u _i = -1 (exit surface)
is.

If the imaging lens has a uniform thickness and the entrance surface has the same geometry as that Has exit surface, the impact of changes in curvature at the entrance and Pick up the exit surface so that the Individual rays are not subject to any deviation.

While the above conclusion refers to an axial ray, it also applies to extra-axial oblique rays, whereby the following condition must be met:

being the relationship

applies, and
y _s : image height on the scanning surface;
v _i (y _s ): height above the optical axis of the point at which the main beam passes the lens surface S _i at image height y; and
c _i (v _i ): curvature of the lens surface S _i at height v _i above the optical axis;
is.

It should be mentioned here that the aspherical imaging lens for use in an optical scanner according to the present invention is desirably made by molding plastics because it enables the aspherical surface to be manufactured easily and at low cost. However, if the cooling rate is uneven during the molding process of a lens with plastic, internal scattering can sometimes occur, creating an uneven refractive index profile. Therefore, the inventors examined conditions under which index distribution would not pose a problem. As shown in Fig. 6, it is assumed for the sake of simplicity that the subscan section of the imaging lens 5 is rectangular (the subscan section is a plane that includes the optical axis and that is parallel to the subscanning direction). The lens has a thickness t in the axial direction and a height h in the subscanning direction. It is assumed that the point of origin of the coordinates lies in the center of the cross section of the lens and that the z-axis extends in the axial direction. while the x-axis extends in the subscanning direction.

With a right-angled cross-section, those with the Cooling isothermal curves essentially used for Longitudinal direction parallel and therefore the refractive index profile essentially uniform in the longitudinal direction, however occurs in a direction perpendicular to this longitudinal direction Index distribution on. The index distribution along the Radiation path has no effects on the Imaging characteristics of the imaging lens, any Index distribution that occurs in the vertical direction however, results in a shift in focus or affects the display characteristics. Therefore  the effects of index distribution with decreasing thickness t and decrease in height h.

A numerical analysis was carried out to determine how the cooling rate within the lens can vary with the ratio of its height h and thickness t. In the assumed model, the lens, which had an initial temperature T1, was cooled in an environment of the temperature T2. Figure 7 is a graphical representation of the cooling time required at each point on the x-axis to reach an intermediate temperature of T1 and T2, namely T3 = (T1 + T2) / 2. The horizontal axis of the graph is the x coordinate normalized to h / 2, ie half the lens height, where 2x / h = 0 represents the center of the lens and 2x / h = 1 an edge of the lens in the direction of its thickness. The vertical axis is normalized to the cooling time at the center of a cross-section of the lens in the direction of its thickness (at its origin). Thus, Fig. 7 shows the profiles of the cooling in a direction normal to the beam path direction. Obviously, the larger the value of h / t, the cooling time approaches a constant value near the center of the lens, thereby achieving a more uniform profile of the cooling rate.

Figure 8 shows the refractive index distributions that were actually measured on plastic lenses that were injection molded. Two values, 0.53 and 1.88, were used for h / t. The horizontal axis is the x coordinate normalized to h / t, and the amount of index variation is plotted on the vertical axis, which is related to the refractive index on the optical axis. When h / t = 0.53, the refractive index changed near the optical axis and an experiment with an actual beam passage showed that the index distribution caused the lens to act as a concave lens, such as a "gradient index" lens , with the resulting shifting of the focal point and impairment of the imaging characteristics. On the other hand, when h / t = 1.88, the refractive index near the optical axis was substantially constant, so that when a light beam was passed, there was no deterioration in the imaging characteristics and no shift in the focus.

Thus, firstly, with increasing h / t, a uniform distribution near the center of the lens was achieved, and secondly, good results were obtained when h / t = 1.88. Taking these facts into account, h / t is desirably equal to or greater than 1.88 (h / t ≧ 1.88). Since measurement errors and deviations in the characteristics must be taken into account in practical applications, it is desirable that in the subscan section of the imaging lens 5 shown in FIG. 6 the ratio of h (the height of the lens in the subscanning direction) to t (the height of the lens in the axial direction Direction) has a value greater than 2 (h / t <2). If this condition is met, it is ensured that the deterioration of the imaging characteristics of the lens and the shift of the focal point are suppressed to an extent that no practical problem arises.

The upper limit of h / t depends on the handicraft assets, productivity and the cost of lens manufacturing. in the in general, h / t is set to less than 50 (h / t <50).

Plastic lenses are usually provided with ribs around their effective area to ensure improved stability and castability. The relationship h / t <2 applies even if h contains such ribs, which are identified by reference number 5 in FIG. 9, and similar results are obtained if they are observed.

Another condition to be met by plastic lenses is that their thickness should be as uniform as possible, since irregular thickness can be a cause of internal dispersion. If the thickness t of an imaging lens varies greatly during the molding process with plastic in the effective area of the main scan cross-section, the molten polymer will flow unevenly during casting, causing internal scattering. In order to avoid this problem, the imaging lens in Example 1 is designed so that the effective range of the ratio between the maximum thickness of the lens in the axial direction (t _max ) and its minimum thickness (t _min ) in the same direction is less than 2 (t _max / t _min <2). If this condition is met, the internal scattering occurring in the imaging lens can be reduced to a level that does not cause any practical problems. Ideally, t _max / t _{min is} equal to the unit ( 1 ) and thus the fulfillment of the relationship 1 ≦ t _max / t _min <2 is desirable.

Another feature of the optical scanner according to Example 1 is that a beam supplied to the imaging lens in the The main scan cross section is convergent. If that on the imaging lens incident beam in the main scanning direction parallel or divergent, the imaging lens must be one positive lens of great refractive power to the beam to focus on the scan surface, but the imaging lens then an extremely uneven Thickness profile in the main scan cross section. To solve this problem is avoided, the one inserted into the imaging lens Adjusted beam of Example 1 so that it in The main scan cross section is convergent, so that the imaging Lens has low refractive power to its possible ensure uniform thickness.

It should also be noted that those in Example 1 the imaging lens used is an anamorphic lens which is described in Main and subscanning devices have different axial powers  Has. This feature allows the correction of aberrations in the main scan direction regardless of the correction in the Subscanning device, giving greater scope to the optical Design is available that ensures that the curvature of the Field in both the main and subscan directions can be reduced while the ability to scan at uniform speed is improved. As before mentioned has the imaging lens used in Example 1 the advantage that the shape of the beam spot in the Main scan direction is only slightly deformed to satisfactory to obtain imaging characteristics. This enables the Providing an optical scanner with satisfactory imaging characteristics even then if the imaging lens is made of axially symmetric Surfaces is built up. A remarkable advantage of the Using an anamorphic imaging lens is that aberrational correction in the main scan direction independently performed by that in the subscanning direction can and that the field curvature continues in both scan directions can be reduced. If the field curvature is small, you can the beam will be dimmed to a diameter that is close is at the diffraction limit, and any deformation of the Beam spot or any difference in the imaging Characteristics are pronounced. Therefore, it becomes an anamorphic One can use lens to reduce field curvature greater benefit from the ability of the invention to Providing satisfactory imaging characteristics pull.

As mentioned above, the beam focuses on the reflecting surface of the rotating lens mirror in the Subscan cut. In the example considered, these are Deflection point and the scan surface in the subscan section optically conjugated and therefore remains, even if the rotating lens mirror a tilting reflective Has the position of the beam spot on the surface  Scan surface in the subscanning direction unchanged and it there is no displacement of the scan line.

In addition, the exit surface is that in Example 1 used imaging lens so that the curvature over a cross section parallel to the subscan section continuously along the main scanning direction in the effective Area of the imaging lens changed. With this Design feature can be the curvature of a subscan cut parallel cross section at any point of the effective Area of the imaging lens to a desired value are set, thereby ensuring that the Field curvature in the subscanning direction can be completely corrected can. As just mentioned, the field curvature is reduced contribute to the ability of the present invention to highlight satisfactory imaging characteristics to provide.

It should be mentioned that the surface of the imaging Lens where the curvature changes in the subscanning direction need not be limited to the exit surface and the The curvature of the entrance surface changed in the subscanning direction can be. Anything to correct field curvature in Subscanning is needed is only a degree of flexibility and the imaging lens can be designed so that for at least one of the two surfaces (entry and Exit surface) the curvature in the subscanning direction changed. If this condition is met, the Curvature of the other surface in the subscanning direction on one desired value can be set.

The imaging lens used in Example 1 is so adjusted that the entry surface has a linear Has a subscan cut, and it is one under consideration through the subscan section of the planoconvex lens. A imaging lens, one of two surfaces one  linear subscan section can be easily reduced Costs are produced. If a lens is two optically has curved surfaces, the accuracy of the relative Positioning the two optical axes of these surfaces problematic and achieving an alignment of Both optical axes are absolutely necessary. if the imaging lens when viewed by the Subscan section formed as a planoconvex lens is, the fulfillment of this requirement is not as long necessary as the subscan cut is affected.

As mentioned above, the two are for optics in one Optical scanners require the ability to Scanning at constant speed and flatness an image plane. Another requirement is that Add beam spot size uniformity. Because current Models of optical scanners have a high scanning density and must have a high resolving power growing need to ensure a constant Beam spot size in the effective scanning area. To one Establishing a constant beam spot size must be ensured be that the optics have a constant optical magnification to have.

It is now the special case of providing one constant optical resolution in the subscanning direction discussed. In the example considered, the light beam in the Subscan section in the vicinity of the reflective Surface of the rotating lens mirror focused so that a constant optical magnification between the imaging point near the reflective surface and the imaging point on the scan surface is ensured.

To simplify the present discussion, assume that the imaging lens 5 is a thin lens, as shown in Fig. 10, with the rotating lens mirror omitted because it has no power in the subscanning direction. The following is also assumed: the distance of the beam-deflecting point P from the scanning surface 6 is a, the distance of the beam-deflecting point P from the imaging lens 5 is b, the height above the optical axis in the effective area of the main scan cross section of the imaging lens 5 is y, and the axial deviation of the imaging lens 5 at height y, based on the intersection of the imaging lens 5 and the optical axis, be Δz (y). Since the reflecting surface of the rotating lens mirror substantially coincides with the beam deflection point P, the latter can be regarded as the imaging point. The optical magnification β (y) of the beam in the subscanning direction, which passes at the position at height y above the optical axis, results in:

According to an experiment carried out by the inventors, the resolving power of an optical scanner lost its uniformity when the beam diameter fluctuated by more than ± 20%, and a laser beam printer produced prints of reduced quality, especially in patterns of fine print dots that caused uneven densities, To avoid this problem, the optical magnification β (y) is designed at a desired height y above the optical axis with respect to the axial (on the axis) optical magnification β (0) to meet the following condition:

By calculating this condition and performing an approximation, we get:

Therefore, an optical scanner that provides not only uniformity of the optical magnification in the subscanning direction but also the resolving power can be realized by observing the following condition:

where Δz _i (y) is the axial displacement of the lens surface S _{i of} the imaging lens at height y in the effective area of the main scan cross section and b _{i is} the distance between the deflection point and the lens surface S _i . A laser printer incorporating such an improved optical scanner will produce good quality prints without uneven densities.

Optical data sheets for a typical design of an optical scanner using the concept of Example 1 are given in Tables 1 and 2. The angle through which the lens mirror 4 travels from the beginning to the end of a scan cycle is given as 2ω. The shape of the diaphragm in diaphragm 7 is elliptical and has the dimensions p _x and p _y in the main scanning and sub-scanning direction. The semiconductor laser 1 emits from point S ₁ , the collimator lens 2 has an entry surface S ₂ and an exit surface S ₃ , the cylindrical lens 3 has an entry surface S ₄ and an exit surface S ₅ , the rotating lens mirror 4 has an entry surface S ₆ , a reflective one Surface S ₇ and an exit surface S ₈ , the imaging lens 5 has an entry surface S ₉ and an exit surface S ₁₀ . The diaphragm 7 coincides with the entrance surface S _{2 of} the collimator lens 2 . The symbols of the associated optical parameters in Table 1 have the following meaning: r _i , the radius of curvature of the it surface S _i ; d _i , the axial distance from the it surface to the nearest surface; n ₂ , the refractive index of the collimator lens 2 , n ₄ , the refractive index of the cylindrical lens 5 , n ₉ , the refractive index of the imaging lens 5 , n ₆ and n ₇ , the refractive indices of the rotating lens mirror 4 , r _ix , the Radius of curvature of an anamorphic lens surface in the subscanning direction, r _iy , the radius of curvature of an anamorphic lens surface in the main scanning direction. The radii of curvature of the aspherical surfaces are given as their axis values. The main scan cross section of the imaging lens has an aspherical shape, which is expressed by:

In a coordinate system in which the origin is the intersection of the lens surface with the optical axis, the z-axis extends in the axial direction and the y-axis in the main scanning direction perpendicular to the optical axis. K _i , A _i , B _i , C _i , D _i , and E _i are aspherical coefficients. The exit surface of the imaging lens is such that the curvature of a cross section parallel to the subscan section in the effective area of the imaging lens and the radius of curvature R _{i are} expressed by:

R _i = r _ix + A _ix y ² + B _ix y ⁴ + C _ix y ⁶ + D _ix y ⁸ + E _ix y ¹⁰

where A _ix , B _ix , C _ix , D _ix , and E _{ix are} coefficients.

Table 1

Table 2

Fig. 11 is a cross section of the optical scanner according to Example 1 in the main scanning direction, and Fig. 12 shows in graph form the aberration curves obtained with the optical scanner of Example 1. The field curvature graph shows the aberration in the main scanning direction by the broken line and the aberration in the subscanning direction by the solid line. According to the agreement, the scanning linearity of an imaging lens is expressed by the deviation of the actual image size from the ideal y = fΘ. However, in Example 1 using the rotating lens mirror 4 , the ideal image size is not equal to fΘ. Therefore, an equivalent representation method is used alternatively, in which the deviation from the ideal image size Y = ξΘ is expressed as a percentage, where ξ the measure of the change in image size is expressed as a function of the angle of rotation of the lens mirror 4 with respect to paraxial individual rays. The symbol ω denotes an angle through which the lens mirror travels while the beam point scans the scanning surface from the center to both ends.

Because of the use of aspherical surfaces, the single imaging lens was sufficient to effectively correct the curvature of the field in the main scanning direction, which was kept within ± 2 mm, as shown in FIG . The residual curvature of the field, which varied with an amplitude of about 1-2 mm, was due to the fact that the shape of the main scan cross-section of the imaging lens was assumed to contain only up to 12 orders of aspherical coefficients and that the magnitude of the field curvature could be further reduced by using higher order aspherical coefficients.

The exit surface of the imaging lens 5 was such that the curvature of a cross section parallel to the subscanning section changed continuously in the main scanning direction in the effective area of the imaging lens 5 , which contributed to the effective correction of the field curvature in the subscanning direction, which within a very small range of ± 0 , 2 mm was held, as also shown in FIG .

The amount of change in curvature ρ by the main scan cross-section of the imaging lens 5 and other related parameters are included in the relationship expressed by:

As the graph of Fig. 13 shows, this relationship varies with the height of an image on the scanning surface, the absolute value of which is at most 1.1. The relationship is for the sum of the two aspherical surfaces S ₉ and S ₁₀ and the values of the corresponding parameters in the relationship are listed below.

Table 3

The subscan section of the imaging lens 5 has a rib at the top and bottom, as shown in FIG. 9. The thickness t of the lens was 5.5 mm and its height 14 mm. Since h / t 2.8, there was no focus shift and the imaging characteristics of the lens were satisfactory.

The thickness of the imaging lens 5 in its effective area in the axial direction was a maximum (t _max ) 5.5 mm and a minimum (t _min ) 3.9 mm. Since t _max / t _min 1.41, the imaging lens 5 is of uniform thickness, which ensures the smooth and uniform flow of a molten polymer during the molding of the plastic lens with virtually no internal scatter.

The beam supplied to the imaging lens 5 was convergent and had a focal point located 213.86 mm from its entrance surface towards the scanning surface. Therefore, the imaging lens 5 needs only a small refractive power in the main scanning direction, which contributes to the uniformity of the thickness of the lens.

The amounts of axial displacement of the surfaces of the imaging lens 5 are expressed by:

As the graph of Fig. 14 shows, this expression changes within the effective range of the lens and its absolute value is 0.18 at the maximum. The deviation in the beam spot size that occurred in the subscanning direction was within ± 10% (see FIG. 15), which indicates the uniformity of the resolution.

If necessary, the resolution can be made more even. In the imaging lens 5 used in Example 1, only the exit surface was adapted, so that the curvature of a cross section parallel to the subscan section changed continuously in the main scanning direction. If both surfaces of the imaging lens 5 are adapted to meet this condition, the freedom in the optical design can be increased by an additional degree in the subscanning direction to ensure that the beam spot size in the subscanning direction can be made completely constant. This will be illustrated with reference to the accompanying drawings. According to the design discussed on the previous pages, the imaging lens 5 is bent as shown in Fig. 11 and the line connecting the main points in cross sections which are parallel to the subscan section is also substantially conforming to the bending shape of FIG Curved lens; although this poses no practical problems, the magnification of the imaging lens 5 varies somewhat in the subscanning direction. However, if the radii of curvature of both surfaces of the imaging lens 5 can be set to desired values in any cross section parallel to the subscan section, the main point H can also be set to a desired position by bending, as shown in Figs. 16a-16e. Based on this idea, the radius of curvature in the subscanning direction can be set in such a way that the connection of the main points in any cross section parallel to the subscanning section produces a straight line perpendicular to the optical axis; in this way, the optical enlargement of the imaging lens 5 in the subscanning direction can be made completely constant over the effective scanning area and a constant beam spot size can also be achieved.

Fig. 17 is a perspective view according to Example 2 of the present invention showing the structure of an optical scanner. , A beam emitted from a semiconductor laser 1 light beam is stopped down to a Blendendiaphragma 7, transformed by the collimator lens 2 into a parallel beam and subjected to the focusing action of a cylindrical lens 3, only in the sub-scanning. The beam strikes a reflecting surface of a rotating polygonal mirror 8 serving as a deflecting means. Image formation only occurs in the sub-scan direction near the reflective surface that reflects the beam. The beam is deflected as the polygonal mirror rotates. The deflected beam is subjected to the focusing effect of an imaging lens 5 and forms a beam spot on the scanning surface 6 .

Optical data sheets for a typical design of an optical scanner incorporating the concept of Example 2 are given in Tables 4 and 5. The angle through which the polygonal mirror 8 travels from the beginning to the end of a scan cycle is indicated by 2ω. The shape of the diaphragm in the diaphragm 7 is elliptical and has the sizes p _x and p _y in the main and sub scan direction. The semiconductor laser emits from point S ₁ , the collimator lens 2 has an entry surface S ₂ and an exit surface S ₃ , the cylindrical lens 3 has an entry surface S ₄ and an exit surface S ₅ ; the rotating polygonal mirror 8 has a plurality of reflecting surfaces S ₆ , the imaging lens 5 has an entrance surface S ₇ and an exit surface S ₈ .

The diaphragm 7 coincides with the input surface S _{2 of} the collimator lens 2 . The symbols of the corresponding optical parameters in Table 4 have the following meanings: r _i , the radius of curvature of the it surface S ₁ ; d _i , the axial distance between the iten surface and the closest surface; n ₂ , the refractive index of the collimator lens 2 , nz ₄ , the refractive index of the cylindrical lens 3 , n ₇ , the refractive index of the imaging lens 5 , r _ix , the radius of curvature of an anamorphic lens surface in the subscanning direction; r _iy , the radius of curvature of the anamorphic lens surface in the main scanning direction. The radii of curvature of the aspherical surfaces are expressed by axial values. The shape of the main scan cross section of the imaging lens 5 is aspherical both on the entrance surface and on the exit surface. The exit surface of the imaging lens is such that the curvature of a cross section parallel to the subscan section in the main scanning direction varies continuously in the effective region of the imaging lens 5 . The shape of the surfaces of the imaging lens 5 is expressed by the same formula as in Example 1.

Table 4

Table 5

Fig. 18 is a cross-sectional drawing by an optical scanner according to Example 2 in the main scanning direction and Fig. 19 as a graph of the aberration curves obtained with the optical scanner according to Example 2. Due to the use of aspherical surfaces, the single imaging lens 5 was sufficient for an effective correction of the curvature of the field in the main scanning direction, which, as shown in FIG. 19, was kept within ± 2.1 mm. The exit surface of the imaging lens 5 was such that the curvature of a cross section parallel to the subscan section along the main scanning direction varied continuously in the effective area of the imaging lens 5 , which effectively corrected the field curvature in the subscanning direction within the very small range of ± 0.1 mm was contributed, as also shown in FIG. 19.

The amount of change in curvature ρ by the main scan cross-section of the imaging lens 5 and other related parameters are included in the relationship expressed by:

As the graph in Fig. 20 shows, this relationship varies with the height of an image on the scanning surface and has an absolute value of 0.12 at most. The relationship applies to the sum of the two aspherical surfaces S ₇ and S ₈ and the values of the corresponding parameters are listed below.

Table 6

The axial displacement values of the surfaces of the imaging lens 5 are expressed by:

As the graph of Fig. 21 shows, this expression varies within the effective range of the lens and its absolute value is not larger than 0.2 at the maximum. The change in beam spot size that occurred in the subscanning direction was kept within ± 2% (see Fig. 22), indicating the uniformity of the resolution.

The optical scanner according to the present invention is not only applicable to laser printers, but also to Image input devices for use with imaging devices Apparatus such. B. digital copiers, fax simile equipment and laser scan displays, as well as with optical symbol lasers and laser equipment for surface inspection, the outstanding advantages can also be achieved.

As described on the previous pages, the optical scanners according to the present invention following remarkable advantages.

The deformation of a steel point can be up to a level be suppressed, which does not cause any practical problem.  

The beam spot size can be kept constant, what the uniform resolution of the optical scanner is helpful is.

The refractive index distribution becomes a radiation path vertical direction is reduced, which is effective in preventing the focus shift or impairment of the imaging characteristics.

The tendency of a melted synthetic polymer to flow unevenly during lens pouring inhibited the production of lenses of good characteristics, that are free from the development of internal dispersion, too enable.

The imaging lens only needs a small one Refractive power and consequently the thickness of the lens can be up to close be brought to uniformity from the standpoint of Productivity and cost is very beneficial.

The correction of aberrations in the main scanning direction can performed regardless of the correction in the subscanning direction become what a greater degree of freedom in optical Design contributes. As a result, the field curvature in both main and subscan directions down to small degrees be suppressed and at the same time the scanning property improved at uniform speed.

The position of a beam spot on the scan surface in Subscanning direction does not change even if the rotating polygonal mirrors or lens mirrors one has tilting reflective surface, and consequently a shift of the scan line can be prevented.

The curvature of a parallel to the subscan section  Cross section can be anywhere in the effective range of imaging lens can be set to a desired value what a complete correction of the field curvature that in the Subscanning may occur.

The imaging lens is easy to make what to contributes to reduced production costs. There is also no more need, high precision in the relative Adhere to the position of the optical axes of the two lenses or an alignment between the two optical axes to reach. This is of great benefit from a standpoint efficient assembly and lens precision.

The degree of freedom in optical design can be in the Subscan direction can be further increased, which in the generation of really constant pixel sizes in the Subscanning helps.

Claims (10)

1. Optical scanner, with
a light source ( 1 ) for emitting a light beam;
deflecting means ( 4 ) which deflect the beam as it rotates at a uniform angular velocity; and
an imaging lens ( 5 ) with aspherical surfaces in a main scan cross section to form a beam spot on a scan surface by focusing the light beam which has been deflected by the deflection means ( 4 ),
characterized by
that the aspherical surfaces of the imaging lens ( 5 ) with respect to the parameters e, n, w, and ρ meet the following conditions:
being the relationship
applies, and
c _i (v _i ): curvature of the lens surface S _i at height v _i above the optical axis;
e _i : distance between lens surface S _i and the scan surface;
g: main scanning radius of the beam spot at zero image height;
n _i : refractive index of the imaging lens forming the lens surface S _i ;
S _i : i th lens surface;
u _i : coefficient indicating whether the lens surface S _{i is} an entrance or an exit surface;
u _i = 1 (entrance surface)
u _i = -1 (exit surface)
v _i (y _s ): height of a point at which the main beam crosses the lens surface S _i at an image height y _s above the optical axis;
w _i : main scan cross-sectional radius of a light beam on the lens surface S _i , which runs along the optical axis of the lens surface S _i ;
y: coordinate representing the height above the optical axis in the main scanning direction;
y _s : image height on the scanning surface; and
ρ _i (y _s ): measure of the change in curvature at the point where the main beam at image height y _s crosses the lens surface S _i , calculated by deriving the curvature c _i to y,
mean. 2. Optical scanner according to claim 1, characterized in that it further fulfills the following condition in a region of the main scan cross section of the lens surface S _{i of} the imaging lens:
in which
Δz _i (y): the axial displacement of the lens surface S _i at a height y above the optical axis,
b _i : the distance between a deflecting point of the deflecting means and the lens surface S _i , and
a: the distance from the deflection point to the scan surface
is. 3. Optical scanner according to one of the preceding claims, characterized in that it further fulfills the following condition in a subscan section of the imaging lens:
h / t <2
in which
t: a thickness of the imaging lens in an optical axis direction, and
h: the height of the imaging lens in the subscanning direction
is. 4. Optical scanner according to one of the preceding claims, characterized in that it further fulfills the following condition in a region of the main scan cross section of the imaging lens:
t _max / t _min <2
in which
t _max : the maximum thickness of the imaging lens ( 5 ) in a direction of the optical axis, and
t _min : the minimum thickness of the imaging lens ( 5 ) in the direction of the optical axis
is. 5. Optical scanner according to one of the preceding claims, characterized in that the light beam incident on the imaging lens ( 5 ) is convergent in the main scanning direction. 6. Optical scanner according to one of the preceding claims, characterized in that the imaging lens ( 5 ) has different refractive powers in the main and subscanning direction. 7. Optical scanner according to one of the preceding claims, characterized in that a deflection point and the scanning surface ( 6 ) are optically conjugated in the subscanning direction. 8. Optical scanner according to one of the preceding claims, characterized in that the curvature of a cross section parallel to the subscan section changes continuously in the main scanning direction in a region of the imaging lens ( 5 ) in at least one of its surfaces. 9. Optical scanner according to one of the preceding claims, characterized in that the subscanner cut in at least one of the surfaces of the imaging lens ( 5 ) is straight. 10. Optical scanner according to one of the preceding claims, characterized in that the curvature of a cross section parallel to the subscan section changes continuously in the main scanning direction in a region of the imaging lens ( 5 ) in its two surfaces.